Wheel Rotation Driver
This set-up is only good if you are going in a straight line. You have not said anything about parenting or driver settings. By looking at your gifs, I can assume you have the wheel parented to the Empty, and your driving the wheels 'X' rotation with the Emptys 'Y' location in 'Local' space, Am I correct so far ?? Even if you change the drivers space to 'World' or 'Transform' - you will still have a 'Coordinance' issue. So then you start thinking , I will use an armature bone(s) - well you will run into the same 'Coordinance' issue again. This issue has been highly debated over at BA for many years, we refer to it as 'the tank track issue', it is a shame that something so basic is so troublesome. So clockmender wrote an animation node to overcome this issue, but if A/N is not your thing, then this is my solution I use; I create 3 actions for the wheel, (1) START (2) TRAVEL (3) STOP -- You can combine these into one action, but I find this way more flexible. You assemble those actions in the NLA, then all you have to worry about is animating the steering. Hope this helps in some way.